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Should a question with false information be downvoted if the OP is just naive and doesn’t know they’ve worked false information into their claim? How about if a question doesn’t make sense because of this is there a way to check in with them before they lose rep (of no fault of their own when they are genuinely trying to produce a good, valid question)?

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    $\begingroup$ Since this got a downvote: I’m not taking a stance or am frustrated about one of my questions, I’m just wondering. $\endgroup$ – Benjamin Thoburn Jan 21 at 23:32
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    $\begingroup$ It's a reasonable Question for meta discussion: what are some good ways to deal with Questions premised on false information or misunderstandings. There are many occurrences of this that show up in the Review Queues. A short response here is that I would try to clear up the misunderstanding by Comments posed as "requests for clarification" in a respectful way. If interested I'll post a longer reply. $\endgroup$ – hardmath Jan 21 at 23:36
  • $\begingroup$ Personally, my recommendation would be to correct them somehow by pointing it out in the comments, and having them append a notice to the top of their post regarding the incorrect info. But I feel like this is also something that would be situation-specific: some concrete examples would help, imo $\endgroup$ – Eevee Trainer Jan 22 at 1:00
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    $\begingroup$ A recent example which comes to my mind: math.stackexchange.com/questions/3068959/… $\endgroup$ – Clarinetist Jan 22 at 13:15
  • $\begingroup$ Here's an example I found in a First Post review, Proving that sequence is decreasing, which hinges on a mistake in signs. This error gets pointed out in comments, but still enough of the how-to-prove-it aspect remains to deserve good Answers. $\endgroup$ – hardmath Jan 22 at 17:32
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    $\begingroup$ Best is to interact via comments. If the comments are ignored then apply a downvote with comment (the chance of ignoring this is reduced, but be prepared for what ensues after that). I keep editing mostly to typos/latex. Editing someone else's post significantly is something which I don't prefer. $\endgroup$ – Paramanand Singh Jan 23 at 9:03
  • $\begingroup$ @Paramanand this makes the most sense to me. $\endgroup$ – Benjamin Thoburn Jan 23 at 12:39
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    $\begingroup$ Maybe leave a comment showing them the flaw in the premise, and if possible correct it and then solve it? $\endgroup$ – Hiten Jan 23 at 16:19
  • $\begingroup$ @postmortes I'd encourage you to undelete your answer, as I think it contributes nicely as a response to the question. $\endgroup$ – Namaste Jan 24 at 15:48
  • $\begingroup$ @amWhy thank-you for the encouragement, but I think your answer both covers everything I wrote more elegantly and eloquently, and goes further into the discussion. Overall, it's significantly better (I upvoted you, for what it's worth) $\endgroup$ – postmortes Jan 25 at 13:53
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When a question contains one or more false premises that is/are inconsistent with what a user aims to prove, or if a question does not make sense in one way or another, then one obvious and perfectly valid course of action is for a user to vote to close the question as "unclear what you are asking", which asks the asker to "Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the "how to ask" page for help clarifying this question."

A comment could be added asking for clarification or asking the asker to check the question they likely transposed, or to point out a false premise and why, and that from false premises, anything follows.

The reasons for downvoting, per the SE network, are given when one hovers over the down-arrow to the left of such a question: "This question does not show research effort, is unclear, or not useful." So if a question does not make sense for any number of reasons, is unclear, or begins with false premises and hence is not useful, it is perfectly appropriate to downvote the sorts of questions you describe, in addition to, or instead of, voting to close the question.

Ideally, one or more users will also, or instead, offer some explanation for the asker, if nothing else, via the information given in the provided close reason after such a question is closed, and additionally, pointers instructing the user as to why the question was closed, and what they can do to fix it, and perhaps get the question reopened.

I do caution users to avoid editing such a question based on a "guess" as to what the user "must mean", or "could have meant", or "probably meant," or based on a "guess" about what "appropriate" premise should replace the given false premise. None of us are mind-readers. Clarification is the job of the asker, though it is certainly helpful to provide the asker with helpful prompts and requests for clarification in comments below the question. By all means, other users are welcome to improve a post, but only after the asker has taken the time and effort to try to respond to requests for clarification.

Finally, I'll add that I think this question is rather biased and leading, particularly by ending with an appeal to protect askers "before they lose rep (of no fault of their own when they are genuinely trying to produce a good, valid question)"?!

Askers, even new askers, are required to acknowledge their responsibilities for asking a decent question, before they even ask the question. Helpful suggestions for askers of poor questions, when they are new users, are wonderful. Protecting them entirely from consequences for asking poor questions and not responding to helpful suggestions is ultimately irresponsible, particularly if both the best interest of the asker, and the best interest of this site, are our ultimate goals.

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Downvoting such questions is, in my opinion, inappropriate*, for a few reasons. (By "inappropriate" in this context, I don't mean "unethical", so much as "bad for the site and for the community at large".)

(a) We should encourage people to ask questions that reveal their misconceptions, since that way these misconceptions can be addressed.

(b) If it's a common false belief, it's a good question and it's important to help others find this good question by upvoting.

(c) If it's a strange and perverse false belief, just leave the question neither upvoted nor downvoted. It's important to make non-experts feel welcome, since the whole point is to help them learn, which won't happen if they don't feel welcome.

(d) It's easy to answer questions predicated on misconceptions. Just say: "Good question! However, there's some common misconceptions in it that need to be cleared up. The question assumes that FALSE BELIEF. However, this turns out to be untrue; here's an example. EXAMPLE. Fortunately, this common false belief points in the direction of a true and correct principle, namely CORRECTED BELIEF." In light of how easy it is to answer such questions, there's no need to panic and rush prematurely for the down-button.

Here's a hypothetical example of (d) in action.

Good question! However, there's some common misconceptions in it that need to be cleared up. The question assumes that there's no way to put $\mathbb{R}$ and $\mathbb{R}^2$ into bijective correspondence. Though intuitively reasonable, this turns out to be untrue. It was Georg Cantor who first discovered this, making use of the well-ordering theorem to show the existence of a bijection $\mathbb{R} \rightarrow \mathbb{R}^2$, contrary to all intuition.

Actually, this isn't as crazy as it sounds. Most functions you might try to visualize are either continuous, or at the very least, piecewise continuous; they have continuous portions punctuated by small jumps. But not every function is like that; for example, consider the function $f:\mathbb{R} \rightarrow \{0,1\}$ such that $x \in \mathbb{Q}$ implies $f(x) = 1$ and $x \notin \mathbb{Q}$ implies $f(x)$ = 0. If you try to visualize $f$, you'll notice it's discontinuous everywhere. And, it's crazy functions like this that allow us to put $\mathbb{R}$ and $\mathbb{R}^2$ into bijective correspondence.

Although the belief that no such bijective correspondence exists was ultimately proven wrong, nonetheless it points to the way to some true beliefs. For example, there is no continuous bijection from $\mathbb{R}$ to $\mathbb{R}^2$..

But note that even in the continuous world, our intuitions can be deceiving. Continuous surjections from $\mathbb{R}$ to $\mathbb{R}^2$ do, in fact exist.

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    $\begingroup$ Do you run the risk of answering a question that wasn't asked? Your hypothetical example for (d) seems to ignore the question that was posted (granted, you haven't given a particular example of that, so I'm making assumptions that may not be true) in favour of correcting the misconception. It seems to me that it would be better to have a question and answer about the misconception, and then remove the question that cannot have an answer because it's got false predicates. $\endgroup$ – postmortes Jan 28 at 8:23
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    $\begingroup$ @postmortes, the way I see it, you want to offer the information the asker needs. If answering an unasked question does that, go ahead and do it. And if their actual question still makes sense after the misconceptions have been addressed, then you can answer that to. Usually you can both answer their main question while addressing any misconceptions all within one grand narrative, so the problem kind of takes care of itself. $\endgroup$ – goblin Jan 28 at 8:48
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Since amWhy's answer appears to primarily address the OP's second question, in which the question with false premises is unclear due to those premises, I'd like to add an answer that addresses the OP's first question, in which the question is not necessarily unclear.

First the points of agreement with amWhy's answer (as I understand the answer):

  1. If a question is unclear, it is perfectly reasonable to downvote and vote to close as unclear.
  2. Do not edit guesses as to what the OP meant into the question. That is the job of the asker.
  3. I agree that this question on meta comes across as biased, although (imo) still overall a decent question for meta.

I'd like to expand on this third point and respond to what the OP wrote

"How about if a question doesn’t make sense because of this is there a way to check in with them before they lose rep (of no fault of their own when they are genuinely trying to produce a good, valid question)."

On to the body of my answer

It has been my experience/impression on this site that people are unlikely to downvote your question because it has an incorrect assumption. People are very likely to downvote your question if you arrogantly assume that you cannot have any errors in your assumptions. People are very understanding if you present your question in the form:

"This is what I've done, and somehow I've arrived at a contradiction or a counterintuitive result. What did I do wrong?"

The problem is with questions of the following form:

"This is what I've done. I've disproved X important fact or shown that Y useful definition is in fact bad or false, what should be done about it?"

An example of a question of this form (since deleted by OP) is this one.

The worst questions of this form are incoherent messes of false assertions that appear to be put there as a half-hearted attempt at providing "context". This question seems to be a good example of this (where the OP asserts that they know that "open map to open" under continuous maps, and that they're looking for a counterexample to this very claim they "know").

A point of clarification on what I think should be done with certain questions with false premises

Questions with false premises shouldn't always be closed, even if they are bad questions in the first sense above in terms of the askers attitude. Such questions are often examples of the XY problem (link to SE meta question on the topic), and as long as they have sufficient context to determine what the OP is confused about, then in my opinion they are clear questions and have non-opinion-based answers that are perfectly valid to give. I.e. it is reasonable to answer such a question by addressing the point of confusion the OP has rather than directly answering the stated question (though if you have not rendered the question irrelevant by addressing the question you should). See here for more a SE meta question on this (targeted more towards programming admittedly).

As an example, consider the first (deleted) question I linked above. It clearly displays two common misconceptions about the difference between polynomials and functions, as well as the difference between isomorphism and set theoretic equality. I think an answer addressing these two points would have been beneficial to the site (and as such was in the middle of writing one when the OP deleted the post, which is why I am aware of it at all). While the question was bad, and thus worthy of downvotes, it was appropriate for this site. I.e., it was on topic, had adequate context, displayed clearly points which could be well addressed by a non-opinion-based answer. Arguably the point about polynomials being different than functions could have qualified it for closure as a duplicate of at least two questions on the topic, however I think the misconceptions about the usage of set theoretic equality in place of isomorphisms qualified it to remain open.

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  • $\begingroup$ "Such questions are often examples of the XY problem (link to SE meta question on the topic), and as long as they have sufficient context to determine what the OP is confused about, then in my opinion they are clear questions and have non-opinion-based answers that are perfectly valid to give." Sure, "as long as they have sufficient context to determine what the OP is confused about," they can address the confusion, best done in comments. My answer addressed the question posted here, about questions with false premise(s), or very unclear. And my answer addressed that question... $\endgroup$ – Namaste Jan 25 at 15:58
  • $\begingroup$ I did not address questions for which answerers "have sufficient context to determine what the OP is confused about." So I suggest you there is no point of objection here (as you state it is), but rather, just your misconstruing the scope of my answer. $\endgroup$ – Namaste Jan 25 at 15:59
  • $\begingroup$ @amWhy Ah, I see, that was indeed a misinterpretation of the scope of your answer then. Perhaps due to a difference in reading of the OP's original question. I read it as two questions, the first asking generally about questions with false premises and what should be done about those, and the second about more specifically what should be done when they are completely unclear (due to the false premises). As I understand what you've written in your answer, I completely agree with you about what should be done when the false premises result in an unclear question. $\endgroup$ – jgon Jan 25 at 16:01
  • $\begingroup$ @amWhy I have edited to indicate less disagreement with your answer. $\endgroup$ – jgon Jan 25 at 16:05

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